Chapter 18 - Gravitational fields

Question 1

what is the range of gravity

Answer 1

infinite

Question 2

Closer gravitational lines mean

Answer 2

stronger field

Question 3

define gravitational field strength, g

Answer 3

gravitational force experienced per unit mass by an object at that point in a gravitational field

Question 4

equation for g

Answer 4

F/m

Question 5

What is the only condition for the equation for g

Answer 5

the object needs to be small enough that the internal gravitational field is negligible compared to the external gravitational field

Question 6

Newtons law of gravitation

Answer 6

two point masses attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of their separation

Question 7

Newtons equation for gravitation

Answer 7

F = -GMm/r^2

Question 8

why is the G minus in the equation for gravitation

Answer 8

gravity is an attractive force

Question 9

gravitational field strength for a point mass

Answer 9

g = GM/r^2

Question 10

Keplers first law

Answer 10

the orbit of a planet is an ellipse. with the sun at one focus, however the eccentricity of the ellipse is very low so the motion can be modeled as circular

Question 11

Keplers second law

Answer 11

a line segment joining a planet and the sun sweeps out equal areas during equal time intervals

Question 12

Keplers third law

Answer 12

the square of the orbital period T is proportional to the cube of the average distance r from the sun. T^2 α r^3

Question 13

How does keplers second law stand

Answer 13

objects move faster when it is closer to the sun

Question 14

derive equation regarding period of orbit for keplers laws

Answer 14

F = mv^2/r = GMm/r^2
GM/r = v^2
as v = 2πr/T
GM/r = 4πr^2r^3/t^2
T^2 = 4π^2r^3/GM
where M is the solar mass
T is the period of orbit
therefore T^2 α r^3

Question 15

What is a satellite

Answer 15

an object orbiting another object, e.g. moon or ISS

Question 16

Outline a geostationary satellite

Answer 16

• have an orbital period of one day
• travel in the same direction as the rotation of the earth
• Travel along the equatorial plane
• remain above the same point on the earths surface
• useful for communications and surveying as they have constant coverage

Question 17

define gravitational potential, Vg with equation

Answer 17

work done per unit mass to move an object from infinity to that point
V(g) = -GM/r

Question 18

what causes a change in gravitational potential

Answer 18

moving towards the object reduces gravitational potential

moving away increases potential

Question 19

Define gravitational potential energy

Answer 19

E = mV(g) = -GMm/r, work done in moving a mass from infinity to that point in a gravitational field

Question 20

Escape Velocity

Answer 20

For an object to escape a gravitational field produced by a mass, the kinetic energy of the object at the start must be equal to or greater the the GPE required to lift it to infinity. Therefore the speed required to exit the gravitational pull.

Question 21

derive equation for escape velocity

Answer 21

KE = 1/2mv^2 = GMm/r

so v = √(2GM/r)